Workthrough Thoughts

on p. 193

"Note that a language may be an infinite set; each string in the language, however, is finite."

Question:

Can you have a set that supports infinite strings? Not an infinite number of strings, but strings that are themselves infinite?

Is a string of infinite length even a reasonable concept to propose?

If a "length" is infinite, can it even reasonably be said to be a "length"?  ... more like a lack of length?
(More musings: Maybe "lack of length" is reserved for the empty string, which has no length? Though I suppose a length of 0 is indeed a length. Just a 0 length.)

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I know that x^2 >= 2x  so long as x >= 2, we've proved that.
But now to show that x^2 > = 2x - 1 so long as x > = 0 ?

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Got it!
x^2 >= 2x  is stronger than x^2 > = 2x - 1
So x^2 >= 2x -1 is already true for all x >= 2.
The only additional cases you need to consider to get from true for all x >= 2  to true for all x>= 0 are 0 and 1. These can be shown directly.